This invention relates to color creation and matching.
Luminaires or light fixtures are capable of reproducing a wide gamut of colors by combining light from, for example, a plurality of LED light sources. However, conventional methods for controlling the output of such luminaires are often unable to accurately reproduce a desired color. The output of the luminaire is limited by, among other things, the number of light sources included in the luminaire and the respective outputs of those light sources.
A convenient way of visualizing the color gamut of a luminaire is using the International Commission on Illumination (“CIE”) 1931 color space chromaticity diagram 10 illustrated in FIG. 1. The CIE 1931 color space chromaticity diagram 10 is a two-dimensional representation of the colors in the visible spectrum in which each color is identified by an x-y coordinate (i.e., (x, y)). The CIE 1931 color space incorporates the use of tristimulus values that correspond to the amounts of three primary colors in a three-component additive color model that are needed to match a target color. The tristimulus values, denoted by X, Y, and Z, are derived parameters that are used to represent the human eye's response to red, green, and blue colors.
The tristimulus values are dependent on an observer's field-of-view (“FOV”). To eliminate this dependence, a standard observer is defined which corresponds to a 2° FOV. The standard observer is described numerically with respect to three color matching functions given by x(λ), y(λ), and z(λ), as shown graphically in diagram 15 of FIG. 2. The color matching functions are used to calculate the tristimulus values X, Y, and Z, as shown below.
                              X          =                                    ∫              0              ∞                        ⁢                                          I                ⁡                                  (                  λ                  )                                            ⁢                                                x                  _                                ⁡                                  (                  λ                  )                                            ⁢                                                          ⁢                              ⅆ                λ                                                    ,                            EQN        .                                  ⁢        1                                          Y          =                                    ∫              0              ∞                        ⁢                                          I                ⁡                                  (                  λ                  )                                            ⁢                                                y                  _                                ⁡                                  (                  λ                  )                                            ⁢                                                          ⁢                              ⅆ                λ                                                    ⁢                                  ⁢                  and          ,                                    EQN        .                                  ⁢        2                                Z        =                              ∫            0            ∞                    ⁢                                    I              ⁡                              (                λ                )                                      ⁢                                          z                _                            ⁡                              (                λ                )                                      ⁢                                                  ⁢                          ⅆ              λ                                                          EQN        .                                  ⁢        3            
The chromaticity of a color is then defined in terms of an x-y coordinate. The Y tristimulus value is used as a measure of brightness or luminance. The x-y coordinate can be calculated as a function of the tristimulus values X, Y, and Z, as shown below in EQNS. 4-6.
                              x          =                      X                          (                              X                +                Y                +                Z                            )                                      ,                            EQN        .                                  ⁢        4                                          y          =                      Y                          (                              X                +                Y                +                Z                            )                                      ⁢                                  ⁢                  and          ,                                    EQN        .                                  ⁢        5                                z        =                              Z                          (                              X                +                Y                +                Z                            )                                =                      1            -            x            -            y                                              EQN        .                                  ⁢        6            
The color space specified by the x-y coordinate and the Y tristimulus value, known as the CIE xyY color space, is often used to identify colors.